Romelu Lukaku scored two superb goals to give Everton a 2-0 FA Cup quarter-final victory on Saturday over his former club Chelsea, for whom Diego Costa was sent off.

As a fractious match neared its conclusion, Lukaku took a Tom Cleverley pass in his stride after 77 minutes and powered past four defenders before burying an unstoppable shot into the back of the visitors' goal.

Just five minutes later, after neat passes from Gareth Barry and Ross Barkley, it was left to Lukaku to deliver the killer blow with another emphatic finish that earned Everton a place in the semi-finals.

The controversy was still to come, however, as Costa earned a second yellow card after 84 minutes as he reacted to a Barry foul by motioning his head towards the Everton man and apparently threatening to bite him.

Barry did not cover himself in glory and after being booked for his part in that flashpoint, he received a second yellow three minutes later for a foul on Cesc Fabregas, which meant that both teams finished with 10 men.

Defeat brought an end to a miserable week for Chelsea, who were eliminated from the Champions League by Paris Saint-Germain on Wednesday and no longer have any chance of winning any silverware this season.

Everton's new co-owner Farhad Moshiri was in attendance at Goodison Park for the first time since paying a reported £200 million ($287.7 million, 258 million euros) to buy 49.9 percent of the club, having made a pre-match address to supporters in the media.

In it, he talked of investment in players, as well as a pledge to hold onto existing talent and solve the club's search for a new state-of-the-art stadium.

But the future of manager Roberto Martinez was not on the agenda, despite disquiet among Everton supporters over the club's current 12th-place standing in the Premier League.

There was little for the home fans to cheer in the early stages, apart from a first-minute Cleverley volley into the body of Chelsea goalkeeper Thibaut Courtois.

Costa was the victim of a crude early foul from Barry and retaliated within seconds, earning a caution as he challenged the Everton midfielder with a leading arm.

Chelsea left-back Kenedy was fortunate not to be cautioned after two clumsy trips on Aaron Lennon, while Costa made the most of slight contact with home defender Phil Jagielka off the ball, appealing for a penalty that was instantly rejected.

Nor were Everton blameless, with Jagielka booked just before the interval for a wild kick at Fabregas.

From the ensuing free-kick, Joel Robles made the first meaningful save of the game by tipping over a dipping effort from Willian.

Courtois was also pressed into action before the interval, diving smartly to make a routine stop from another long-range Cleverley shot.

Chelsea's goal was threatened again soon after the restart, Ramiro Funes Mori rising well to meet a Cleverley corner with a header that just cleared the crossbar.

Chelsea finally showed some attacking intent, after 56 minutes, and almost scored from their first meaningful foray into Everton territory.

Fabregas found Costa, who beat Funes Mori and rounded Robles, only to steer a low shot across goal and wide from a difficult, narrow angle.

Courtois was again pressed into action when he rushed from his line to dispossess Lukaku, but the Belgian striker, sold by Chelsea in 2014, would have the last laugh.